We establish a geometric quantization formula for a Hamiltonian action of a compact Lie group acting on a noncompact symplectic manifold with proper moment map.

EXPONENTIAL LAW FOR UNIFORMLY CONTINUOUS PROPER MAPS R . AYALA, E . DOMINGUEZ, A . QUINTERO The purpose of this note is to prove the exponential law for uniformly continuous proper maps . Let X be a regular space and Y a locally compact regular space . It is well known that the spaces of continuousmaps C(X x Y, Z) and C(X, C(Y Z)) are homeomorphic considering the compact-open topology. This pro...

We present a survey on recent study of special continuous maps, like biquotient, triquotient, proper, perfect, open and étale maps and a selection of open problems in this area. 1. Special morphisms of Top Triquotient maps were introduced by E. Michael in [24] as those continuous maps f : X → Y for which there exists a map ( ) : OX → OY such that, for every U, V in the lattice OX of open subset...

We generalize Marshall Cohen's notion of transverse cellular map to the polyhedral category. They are described by the following: Proposition. Let f : K —* L be a proper simplicial map of locally finite simplicial complexes. The following are equivalent: (1) The dual cells of the map are all cones. (2) The dual cells of the map are homogeneously collapsible in K. (3) The inclusion of L into the...

In this article, we study local holomorphic isometric embeddings from Bn into BN1 × · · · × BNm with respect to the normalized Bergman metrics up to conformal factors. Assume that each conformal factor is smooth Nash algebraic. Then each component of the map is a multi-valued holomorphic map between complex Euclidean spaces by the algebraic extension theorem derived along the lines of Mok and M...

In this article, we study local holomorphic conformal embeddings from B into B1 × · · · ×BNm with respect to the normalized Bergman metrics. Assume that each conformal factor is smooth Nash algebraic. Then each component of the map is a multi-valued holomorphic map between complex Euclidean spaces by the algebraic extension theorem derived along the lines of Mok and Mok-Ng. Applying holomorphic...

Sensory processing requires proper alignment of neural maps throughout the brain. In the superficial layers of the superior colliculus of the midbrain, converging projections from retinal ganglion cells and neurons in visual cortex must be aligned to form a visuotopic map, but the basic mechanisms mediating this alignment remain elusive. In a new mouse model, ectopic expression of ephrin-A3 (Ef...

ecotourism as the most attractive subset of the tourism industry can contribute to natural resource conservation and local development. although great numbers of people annually visit abbasabad area, in veresk, mazandaran, to enjoy its brilliant landscape and moderate ecologic condition, there is no applicable plan for many natural attractive zones in this area. as a result, some specific well ...